One way is just to listen for it... Phase problems can make your audio sound thin or tonally uneven (certain frequencies might sound like they're repeatedly dropping out and coming back in). You can sometimes hear them more easily by switching the signal to mono, since stereo phase problems will cause some sounds to get much quieter, or even disappear, in mono mixes.

Another way to spot them is by using a phase analysis plugin. Waves PAZ Position is one such plugin which does a really good job, and some multi-purpose plugins (like Izotope's Ozone) have a different kind of phase meter, which leans to one side more often as phase problems occur. There are probably cheaper or free plugins out there that show phase problems too, I just don't know any offhand...

I woudn't worry so much about knowing as much as I would by flipping polarity on anything you are worried about and then listen for which way sounds better. Does it still sound ok in mono? So what if something is out of phase with something else if it sounds best to you?

Another way to spot them is by using a phase analysis plugin. Waves PAZ Position is one such plugin which does a really good job, and some multi-purpose plugins (like Izotope's Ozone) have a different kind of phase meter, which leans to one side more often as phase problems occur.

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Those "phase" meters are more about whether or not you have a balance of level from left to right than real phase... though if you actually know how to read one they can be quite informational.

Understand that recorded sound is a function of energy [level] vs. frequency, vs. time... time is where you can have phase anolomies... the majority of these phase anomolies occur in an exceptionally short period of time... in the .01ms to .1ms range... though they can [and will occur all the way out to the 21ms range, once they get past like .3ms it's really a time based thing that you can often just fix by sliding a track in a DAW... but I digress].

Phase anomolies manifest themselves most often as a boxiness in the midrange, or a rather "haw" sounding vowel kind of thing that is added to a note/sound. This most often occurs when you have two or more mics on a single source [like two mics on a guitar cabinet, or trying to record bass via a mic and a DI]... the human ear percieves these time differences as part of the original signal, which is percieved as a comb filtered event.

Now... there is also the 180' out of phase thing [which is really being electronically out of polarity... but it's often referred to as "out of phase"]. If you're talking about something like a pair of speakers being out of polarity, you will notice two things... first, the low frequencies will all but disappear, the second will be a rather nauseating feeling brought on by your head moving through the spots where different frequencies from the speakers add and subtract... kinda makes your head wanna spin around like Linda Blair's in the Excorcist.

If you're talking about two signals being 180' out of polarity within a mono signal path... you will notice that when you get them level matched they will cancel... like you can bring up a second fader until you get absolutely nothing for an output [this is the way you set up the "S" part of an "M-S" pair].